Question

How do you find 3tan^3x=tanx?

Answer 1

Simplify both sides with tanx
3tan^2x=1 , tan^2x=1/3
and root both side , \[\left| tanx \right|=1/\sqrt{3}\]
So go on from here

Answer 2

thank you!

Answer 3

No, don't do that. Unless you want to lose half your solutions.

Answer 4

\[3\tan^3x = \tan x \iff \tan x\ (3\tan^2x -1) = 0\]
\[\implies \tan x = 0 \implies x = ...\]
OR
\[\implies \tan^2x = \frac{1}{3} \implies \tan x = \pm \sqrt{\frac{1}{3}}\]